Theorems · Theorem · ring theory
Finsupp.sum_single
∀ {α : Type u_1} {M : Type u_8} [inst : AddCommMonoid M] (f : α →₀ M), f.sum Finsupp.single = f- Cited by
- 19 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Finsuppstatement and proof · cited by 5,255
- Finsupp.singlestatement · cited by 943
- Finsupp.sumstatement · cited by 481
- DFunLike.congr_funproof · cited by 288
- Finsupp.liftAddHom_singleAddHomproof · cited by 1
Cited by19
Results whose statement or proof uses this declaration.
- Module.Basis.repr_symm_applyproof · cited by 37
- MvPolynomial.monomial_eqproof · cited by 20
- Finsupp.mapDomain_idproof · cited by 13
- SkewMonoidAlgebra.sum_singleproof · cited by 7
- AddMonoidAlgebra.sum_coeff_singleproof · cited by 6
- MonoidAlgebra.sum_coeff_singleproof · cited by 6
- MvPolynomial.support_sum_monomial_coeffproof · cited by 6
- Nat.prod_pow_factorization_eq_selfproof · cited by 4
- Module.Basis.SmithNormalForm.repr_apply_embedding_eq_repr_smulproof · cited by 3
- Finsupp.supported_eq_span_singleproof · cited by 3
- Finsupp.indicator_eq_sum_attach_singleproof · cited by 1
- Ideal.Filtration.submodule_closure_singleproof · cited by 1